TY - JOUR
A2 - Liu, Baoding
AU - Khan, Madad
AU - Feng, Feng
AU - Khan, M. Nouman Aslam
PY - 2013
DA - 2013/01/08
TI - On Minimal Fuzzy Ideals of Semigroups
SP - 475190
VL - 2013
AB - The present paper contains the sufficient condition of a fuzzy semigroup to be a fuzzy group using fuzzy points. The existence of a fuzzy kernel insemigroup is explored. It has been shown that every fuzzy ideal of a semigroupcontains every minimal fuzzy left and every minimal fuzzy right ideal of semigroup. The fuzzy kernel is the class sum of minimal fuzzy left (right) ideals of a semigroup. Every fuzzy left ideal of a fuzzy kernel is also a fuzzy left ideal of a semigroup. Ithas been shown that the product of minimal fuzzy left ideal and minimal fuzzyright ideal of a semigroup forms a group. The representation of minimal fuzzy left(right) ideals and also the representation of intersection of minimal fuzzy left idealand minimal fuzzy right ideal are shown. The fuzzy kernel of a semigroup is basicallythe class sum of all the minimal fuzzy left (right) ideals of a semigroup. Finallythe sufficient condition of fuzzy kernel to be completely simple semigroup has beenproved.
SN - 2314-4629
UR - https://doi.org/10.1155/2013/475190
DO - 10.1155/2013/475190
JF - Journal of Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -